Soaked to the bone and ankle deep in mud, thousands of people seeking refuge in Europe are finding that their path to a new life is growing harder by the hour.

A Syrian refugee kisses his daughter as he walks through a rainstorm towards Greece's border with Macedonia, near the Greek village of Idomeni. (Reuters Photo)

Soaked to the bone and ankle deep in mud, thousands of people seeking refuge in Europe are finding that their path to a new life is growing harder by the hour.

Torrential rains poured as an unprecedented 7,000 trekkers crossed the Greek border into Macedonia on Thursday past rows of camouflage-jacketed police. Children stumbled into mud-filled potholes and had to be pulled back out, bawling, into their mothers' arms. People struggled to find anything - plastic sheets, garbage bags, even a beach umbrella - to shield themselves from an unrelenting deluge.

And yet nothing could dampen their hopes of reaching the heart of Europe, where asylum and border security systems are already in danger of being overwhelmed in the migration crisis.

"I'm not going to be afraid of anything," said Waseem Absi, a 30-year-old from Ariha in northern Syria, as he held a disassembled pup tent over his head and trudged up a muddy slope alongside four friends. He said he hopes to reunite with relatives in the Netherlands.

The sudden onset of autumn has taken tens of thousands by surprise all along the Balkans route from Greece to Hungary, the main gateway to Western Europe for more than 160,000 asylum seekers already this year.

Stuffed toys are seen amongst possessions left behind by migrants and refugees after a rainstorm at the border crossing between Greece and Macedonia, near the Greek village of Idomeni. (Reuters Photo)

As recently as last week, those making the epic journey, much of it on foot, were baking in a region-wide heat wave and free to sleep under the stars. Now they're without shelter and struggling to keep campfires burning, highlighting the inadequate support provided by several European governments at each border crossing.

Conditions also rapidly deteriorated on Hungary's southern border with Serbia, where an estimated 3,000 crossed at an approved rail site or illegally by ducking under the razor-wire marking that frontier. Garbage-strewn fields turned to mud, trapping relief agency trucks whose wheels spun and flecked passing migrants with sodden earth.

With Hungary and other nations providing few facilities on their borders, travelers have poured into the few tents erected recently by relief workers trying to compensate for the lack of government support.

"The medical tent is full of people - people who aren't actually sick, by the way, but just want a warm place to sit down. We can't get rid of them," said Gabor Gyurko, a volunteer for the Catholic charity Caritas, which is providing medical care at a police-supervised collection point.

Medics gave first aid to several mothers and their children and covered them with thermal blankets.

Gyurko said he expected the volume of ill people to surge with the chilly, wet weather "especially among people living in such close quarters."

International aid workers said Hungary has failed to provide sufficient shelter at migrant bottlenecks on the border, particularly near the village of Roszke. The country instead is investing in a new security regime, supposed to begin Sept. 15, designed to close its border with Serbia backed by more than 3,000 troops, many of whom conducted drills Thursday in cooperation with Serbian colleagues.

"The situation here is really a big disaster because a lot of refugees are coming every hour from the border from Serbia to Hungary, to Roszke, and we don't have real infrastructure here," said Kathrin Niedermoser, whose Austrian charity for asylum seekers provided what food it could keep from getting wet. "We have small tents, now it's raining, and all the things are getting wet."

She said Hungary should deploy "big tents where people can come, sleep and have a rest. We don't even have electricity, which means we don't have warm water during the whole day."

Conditions improved farther north on the route. Austrian police said more than 6,000 crossed Thursday from Hungary, chiefly near the town of Nickelsdorf, where authorities struggled to find enough buses, trains and emergency shelter. Most went to nearby towns, but more than 1,000 stayed in huge halls filled with beds near the border.

Earlier, Austria's rail company suddenly canceled all of its cross-border service with Hungary, citing what it called "a massive overload." That raised tensions at Budapest's main Keleti station, where dozens of daily trains were scheduled to reach the Austrian capital, Vienna. Several hundred people from the Middle East, Asia and Africa waited up to 10 hours with tickets in hand as police penned them into one area. Volunteers from the Migration Aid charity used bullhorns to try to reassure the crowd in both Arabic and English that the trains would come.

Confusion reigned as Keleti's huge arrivals and departures board showed many westbound trains to Austria, but two dozen police in surgical masks and gloves - a measure they take fearing the foreigners might have contagious diseases - blocked their access to the platforms. Hungarians and other international passengers were ferried by police along the edge of the asylum seekers to the trains.

As rumors spread that Austria was canceling services, officials scrambled to shift train schedules. After hours without clear information and amid tears of joy and relief, police gradually allowed the crowd through to trains to the border near Nickelsdorf, where they faced short walks to Austrian aid workers.

"My husband is waiting for me in Vienna. I cannot wait to see him," said Nuha al-Gumaa, a native of Aleppo, Syria, who was traveling with two brothers and her four children, including daughters Gaber, 3, and Nadine, 4. "We were on the border (with Serbia) a day ago, but reached here by walking and by bus. We slept in a garden last night. We all want so badly for this journey to be done."

A migrant woman walks with her children on rail tracks as they cross the border between Greece and Macedonia near the town of Gevgelija. (AFP Photo)

The International Organization for Migration reported on Thursday that 432,761 people have entered via Mediterranean routes, either from Libya to Italy or from Turkey to Greece, so far this year. That shattered previous forecasts that such traffic might reach 400,000 by the end of 2015. Germany, the most popular destination for asylum seekers because of Chancellor Angela Merkel's pledge to provide refuge particularly to Syrians, has received more than 30,000 people since Saturday, when it and Austria struck an emergency deal with Hungary to accept thousands who had marched out of refugee camps and Keleti station toward Austria.

But Austria said it was reviewing its policy of permitting Germany-bound migrants to pass through without even registering and expressed hope that Hungary's tougher border measures would allow the country to regain control of its own asylum system.

Denmark initially sought to block hundreds of asylum seekers from trying to pass through the country to Sweden, another top destination because of its strong reputation for welcoming refugees.

But Denmark's police chief, Jens Henrik Hoejbjerg, said the country would permit all asylum seekers to reach Sweden unimpeded. That decision flies in the face of European Union rules that refugee claims should be made in the first EU entry point.

"We can't detain foreigners who do not want to seek asylum here," Hoejbjerg said. "There is no other option than to let them go, and we cannot prevent them from traveling wherever they want."

More than 3,200 had entered Denmark from Germany since Sunday, of which just 668 people have sought asylum, he said.

In the Syrian capital of Damascus, the government of President Bashar al-Assad made a rare comment on the migration crisis, saying Europeans only had themselves to blame for backing rebel groups fighting the government for the past four years.

Information minister Omran al-Zoubi said people mostly were fleeing areas held by anti-government forces, including the Islamic State group. He said Europe "sent terrorists" to Syria and imposed economic sanctions designed to drive people from the country. Government-held territory remained safe, he said, and "any Syrian abroad can return to his country any time he wants."